Vedic maths
Five shortcuts that turn four lines of paper into two steps
These are the techniques ComputePrep's Vedic path drills, one kind at a time, on a 15–45 second clock. Each is worked below — read it once, then practise it daily until it stops feeling like a trick. Two more — division and working-base multiplication — are worked further down as previews: real techniques, not yet a timed drill.
Short answer for anyone in a hurry: the five that actually pay off in a bank or SSC paper are Nikhilam (multiplying near 100), Ekadhikena and Yavadunam (squaring), Antyayordashake (units adding to 10), Sankalana-Vyavakalanabhyam (multiply through the midpoint) and Urdhva-Tiryagbhyam (the general crosswise method). Everything else is a variation on those.
1. Nikhilam — multiplying near a base
When to use it: both numbers sit close to 100 (or 10, 1000).
97 × 96
- Deficits from 100: 97 → −3, 96 → −4.
- Left part — cross-subtract: 97 − 4 = 93 (or 96 − 3 = 93; they always agree).
- Right part — multiply the deficits: 3 × 4 = 12.
- Join them: 93 | 12 → 9312.
The trap, and the one thing to drill: the right part must be exactly as wide as the base has zeros. 88 × 89 gives deficits 12 and 11, so the right part is 132 — three digits where only two fit. Carry the extra: 77 | 132 → 7700 + 132 = 7832. Writing 77132 is the classic error, and it is always sitting in ComputePrep's options waiting for you.
Start a timed Nikhilam drill →
2. Vedic squaring — Ekadhikena and Yavadunam
When to use it: the number ends in 5, or sits near a base.
Ends in 5 — Ekadhikena: take the part before the 5, multiply it by one more than itself, append 25.
75² → 7 × 8 = 56, append 25 → 5625.
85² → 8 × 9 = 72 → 7225.
Near a base — Yavadunam: subtract the deficit again, then append the deficit squared (same carry rule as Nikhilam).
96² → 96 − 4 = 92, 4² = 16 → 9216.
88² → 88 − 12 = 76, 12² = 144 → 7600 + 144 = 7744.
88² is the drill that matters — 98² never teaches you the carry.
Start a timed Vedic Squaring drill →
3. Complementary products — Antyayordashake
When to use it: the two numbers have the same leading part and their units digits add to 10.
43 × 47 — same tens (4), units 3 + 7 = 10.
- Left: 4 × 5 = 20 (the tens digit times one more than itself).
- Right: 3 × 7 = 21 (the units, padded to two digits).
- 20 | 21 → 2021.
Padding matters: 91 × 99 → 9 × 10 = 90, 1 × 9 = 09 → 9009, not 909.
Start a timed Complementary Products drill →
4. Difference of squares — Sankalana-Vyavakalanabhyam
When to use it: the two numbers are equally spaced around a round midpoint.
47 × 53 — midpoint 50, distance 3.
50² − 3² = 2500 − 9 = 2491.
68 × 72 — midpoint 70, distance 2: 4900 − 4 = 4896.
The error the options will offer you is m² + d². It is a plus sign that costs a mark.
Start a timed Difference of Squares drill →
5. Crosswise multiplication — Urdhva-Tiryagbhyam
When to use it: everything else. This is the general method — it multiplies any two numbers in one line, with no special condition.
23 × 41
- Units: 3 × 1 = 3.
- Cross: (2 × 1) + (3 × 4) = 14 → write 4, carry 1.
- Tens: 2 × 4 = 8, plus the carry → 9.
- 943.
The easy variant — × 11: first digit, then the neighbour sums, then the last digit. 43 × 11 → 4 | (4+3) | 3 = 473. With a carry: 87 × 11 → 8 | 15 | 7 → 957.
Start a timed Crosswise Multiplication drill →
6. Paravartya Yojayet — dividing by a number just above a base
When to use it: the divisor sits one more than a round base — 11 (one above 10), 101 (one above 100). This is a preview, not yet a ComputePrep drill — the case shown here (a divisor exactly one above the base) is the clean one; a divisor further above the base can need an extra borrow step this page isn't teaching yet.
1234 ÷ 11 — base 10, divisor 11 = 10 + 1.
- Bring down the first digit as-is: 1 (first quotient digit).
- Multiply the last quotient digit by −1 and add it to the next dividend digit: 2 + (−1×1) = 1 (second quotient digit).
- Repeat: 3 + (−1×1) = 2 (third quotient digit).
- The last digit gives the remainder the same way: 4 + (−1×2) = 2.
- Quotient 112, remainder 2 — check: 112 × 11 + 2 = 1234.
It scales to any length: 123456 ÷ 11 runs the same left-to-right chain across six digits and gives quotient 11223, remainder 3.
7. Anurupyena — multiplying near a working base that isn't a power of 10
When to use it: both numbers sit close to a convenient number that is a simple fraction or multiple of a power of 10 — 50 (= 100 ÷ 2), 25 (= 100 ÷ 4) — rather than close to 10, 100 or 1000 directly. This is also a preview: the case shown here, where both numbers sit on the same side of the working base, keeps the rescaling step a clean whole number. Numbers straddling the base on opposite sides can push that rescaling to a fraction, which needs a borrow between the two parts this page isn't teaching yet.
46 × 48 — working base 50 = 100 ÷ 2.
- Deviations from 50: 46 → −4, 48 → −2.
- Cross-add for the raw left part: 46 − 2 = 44 (or 48 − 4 = 44).
- Rescale the left part for the working base: 50 is 100 ÷ 2, so divide by 2: 44 ÷ 2 = 22.
- Right part — multiply the deviations: (−4) × (−2) = 8, padded to two digits: 08.
- Join them: 22 | 08 → 2208.
Second check — 52 × 54: deviations +2 and +4, raw left 52 + 4 = 56, rescaled 56 ÷ 2 = 28, right part 2 × 4 = 08, joined: 2808.
Which shortcut applies? A ten-second decision
| What you see | Use | Example |
|---|---|---|
| Both numbers near 100 / 1000 | Nikhilam | 97 × 96 = 9312 |
| Number ends in 5, squared | Ekadhikena | 75² = 5625 |
| Number near a base, squared | Yavadunam | 88² = 7744 |
| Same tens, units add to 10 | Antyayordashake | 43 × 47 = 2021 |
| Equal distance from a round number | Difference of squares | 47 × 53 = 2491 |
| Multiplying by 11 | Neighbour sums | 87 × 11 = 957 |
| Anything else | Urdhva-Tiryagbhyam | 23 × 41 = 943 |
| Dividing by a base+1 number (preview) | Paravartya Yojayet | 1234 ÷ 11 = 112 r2 |
| Both near a non-decimal base, same side (preview) | Anurupyena | 46 × 48 = 2208 |
Reading them is not the point
Every aspirant who has watched a vedic-maths video knows these exist. The gap between knowing a shortcut and reaching for it under a clock is where marks are lost, and it closes only with repetition against a timer.
That is the whole reason ComputePrep exists: the Vedic path rotates through these five kinds, three difficulties a day, 15–45 seconds each, with the sutra steps shown after every single drill. It is free, and it takes about five minutes.
FAQ
What is the Nikhilam sutra?
A method for multiplying two numbers that sit close to a base like 100. You subtract crosswise to get the front part of the answer and multiply the two deficits to get the back part — 97 × 96 becomes 93 and 12, joined into 9312, without a single long-multiplication line.
How do you square a number that ends in 5?
Take the digits before the 5, multiply that number by one more than itself, and append 25. For 75²: 7 × 8 = 56, so the answer is 5625. This is Ekadhikena, and it works for any number of digits ending in 5.
What is Antyayordashake (complementary products)?
A shortcut for two numbers that share the same leading digits and whose units digits add to 10 — 43 × 47, for example. Multiply the leading part by one more than itself for the front (4 × 5 = 20), multiply the units for the back (3 × 7 = 21, padded to two digits), and join them: 2021.
Are vedic maths tricks actually worth learning for bank and SSC exams?
Only the ones that match how the paper actually sets its numbers — which is why this page covers five drilled sutras plus two supporting ones, not the dozens sometimes listed online. Knowing a shortcut and reaching for it under a 15–45 second clock are different skills; the second one only comes from timed repetition, which is the whole reason ComputePrep exists.
How does Paravartya Yojayet help with division?
It turns division by a number just above a base (like 11, just above 10) into a left-to-right chain of small multiplications and additions instead of long division. For 1234 ÷ 11: bring down 1, multiply by −1 and add to each next digit in turn, reading off quotient 112 with remainder 2. It scales cleanly to any dividend length.
What is Anurupyena, and why isn't there a timed drill for it yet?
Anurupyena multiplies near a convenient working base other than a power of 10 — 50, for instance, treated as 100 ÷ 2. It is genuinely useful, but the general case (numbers straddling the base on opposite sides) needs a fractional-rescaling step we want to teach carefully before it appears as a timed, auto-scored drill. For now it is here as a worked preview, restricted to the clean case where both numbers sit on the same side of the base.
Take them with you: the free Vedic Speed Kit (PDF) packs all five techniques with engine-verified worked steps, 20 practice problems and the speed tables — yours to keep and forward.
The other half of the paper. Speed handles quant; the reasoning section needs a different muscle. Our sister product Deduce is a daily reasoning puzzle across 27 reasoning types — same makers, same aspirants, same five-minute habit.